Exact Enumeration of Rooted 3-connected Triangular Maps on the Projective Plane (Extended Abstract)

We study the relation between rooted 3-connected triangular maps and rooted 2-connected triangular maps on the projective plane. We then use this relation to derive a simple parametric expression for the generating function of rooted 3-connected triangular maps on the projective plane. We believe that this is the first simple exact result for 3-connected nonplanar maps.